is expansion tank still working properly

Have an expansion tank on the water heater. It is positioned vertically ABOVE the cold horizontal pipe (only place to put it) that runs above the water heater. Is there a way to check it to see if it is still working properly? I read about tapping it, but am not sure what part is supposed to sound hollow, the bottom closest to the water heater or the top part where the little valve is. Thank you for any help. (Plumber said he would charge me $75 to come out and look at it).

An expansion tank, properly setup, is essentially full of air, with maybe a quart or two of water in it after a big use of the hot. It should almost ring like a bell rather than thump like it is full. Two things, if it sounds like it is full of water, it's probably shot. On the bottom of the tank, there's a cap on the air valve (like on a tire). Take it off, and check the pressure. If water comes out, or it is rusty, the tank is probably shot. If no water comes out, note the pressure. Then, shut off the water at the main. Then open a faucet and leave it open. Then check the pressure again. If it is lower than when you checked it, pump it up to that pressure. A bicycle pump works, but be careful not to overinflate it, however you choose to add air. That way, the tank won't see any water until the pressure tries to rise, then it will go into the tank, compress the air in the bladder, and keep the water pressure from rising. Once done, close the faucet, and turn the water main back on.

If your tank is shot, it's easy to replace. Make sure to get one designed for potable water (not a heating system on a boiler), the same size. Adjust the precharge air pressure to your normal valve (noted above), unscrew the old one (careful, it could be heavy if it is full of water), tape or dope on the threads, and thread the new one on, and you're done. Be sure to shut the water supply off before you try to remove and replace and open a valve to relieve pressure first!